If a ^3 +3 a ^2 =m and a ^3 +3 a ^2 =n , then (m+n)^ 2 / 3 +(m-n)^ 2 / 3 is equal to

Step-by-step solution

Given relations are aligned & a ^3 +3 a ^2 =m ...(i) & a ^3 +3 a ^2 =n...(ii) aligned On adding Eq. (i) and (ii) we get aligned (m+n)= & a ^3 +3 a ^2 & +3 a ^2 +a ^3 = & a( + )^3 aligned Similarly on subtracting Eq. (ii) from Eq. (i), we get aligned & m-n=a( - )^3 & Now, (m+n)^ 2 / 3 +(m-n)^ 2 / 3 & =a^ 2 / 3 ( + )^2+( - )^2 & =a^ 2 / 3 2 ( ^2 + ^2 ) =2 a^ 2 / 3 aligned